Oscillators are commonly used in electronic and optical systems to generate an oscillating signal for a wide variety of applications. For example, low phase-noise oscillators, such as opto-electronic oscillators, are used in wireless communication, sensing, spectroscopy, high resolution imaging units, and high resolution radars. FIG. 1 is a simplified block diagram of an opto-electronic oscillator 100, as known in the prior art. Opto-electronic oscillator 100 is shown as including, a laser 120, a Mach-Zehnder modulator (MZM) 110, a delay line 122, a photo-diode 124, a filter 126, and an amplifier 128. The output of amplifier 128 is an oscillating signal OSC and applied as a feedback signal to phase modulator 102 disposed in MZM 110.
The signal generated by laser 120 is delivered to both optical paths 130 and 135 of MZM 110. The optical signal travelling in path 135 is phase modulated by phase modulator 102 and combined by combiner 104 with the optical signal travelling in path 130. In the following, for simplicity, an optical path and the optical signal travelling through that path may be identified using the same reference number. For example, optical path 130 may be alternatively referred to as optical signal 130. If the output signal of phase modulator 102 and optical signal 130 are in phase, combiner 104 causes a constructive interferences of these two signals, thereby to generate a high-level signal at its output. If, on the other hand, the output signal of phase modulator 102 and optical signal 130 are 90 degrees out-of-phase, combiner 104 causes a destructive interferences of these two signals, thereby to generate a low-level signal at its output.
The longer the time delay caused by delay line 122, the smaller is the phase noise. Accordingly, the delay across delay line 122 and the filter characteristics of filter 126 are designed so as to achieve the required level of phase noise and the oscillation frequency. Photo-diode 124 is adapted to convert the optical signal it receives from delay line 122 to an electrical signal. This electrical signal is subsequently filtered by filter 126 and amplified by amplifier 128. The output of amplifier 128 is used a feedback signal to vary the phase of optical signal 135 and provide the oscillation.
The noise contribution from different sources in oscillator 100 may be modeled as an electrical noise current In injected into path 150—which connects photodiode 124 and filter 126, as shown in FIG. 2. The total noise contribution may be defined as following:in,total2=in,electrical2+in,Laser,RIN2+in,Photodiode,shot2  (1)
In the above expression (1) in,electrical represents the total input-referred current noise associated with all the electronic blocks, in,Laser,RIN represents the equivalent current noise associated with the laser's relative intensity noise (RIN), and in,Photodiode,shot represents the photodiode shot noise. For oscillator 100, the −3 dB linewidth of the power spectral density of the generated electrical oscillatory voltage is defined by:
                              C          e                ≈                                            i                              n                ,                total                            2                        _                                2            ⁢                          R              2                        ⁢                          P              0              2                        ⁢                          τ              2                        ⁢                                          J                1                2                            ⁡                              (                                                                            V                      o                                                              V                      π                                                        ⁢                  π                                )                                                                        (        2        )            
In the above expression (2), parameters R, P0, τ, V0, and Vπ respectively represent the photodiode responsivity, the laser power, the delay of the optical delay line, the oscillation amplitude, and the modulator voltage to phase gain, respectively. Also, J (.) represents the Bessel function of the first kind.
Using a typical semiconductor laser in an opto-electronic oscillator, usually the largest noise contribution comes from the laser amplitude noise. As an example and referring to FIG. 1, for a laser with RIN of −130 dB/Hz, photodiode responsivity R≈1A/W, laser power P0=1 mW, and total electrical noise figure of 3 dB, noise parameter in,Laser,RIN which is defined by RP0√{square root over (RIN)} is approximately equal to 316 pA/√{square root over (Hz)} for this example. The equivalent noise associated with the laser is thus an order of magnitude greater than the input referred current noise of electrical circuitry, in,electrical, which for a 3 dB noise figure in a 50Ω system is approximately equal to 17 pA/√{square root over (Hz)} in the above example. As shown with this example, reducing the laser RIN significantly reduces the phase noise of an opto-electronic oscillator.